Republicans counter that they want a budget agreement that tackles “out-of-control” government spending, but see little point in a conference committee if Senate Democrats continue to demand a trillion dollars in new taxes while refusing to compromise on cuts.

“House Republicans want an agreement, and conversations are continuing to build a framework for constructive negotiations. But until we have that framework, establishing a conference committee won’t bridge the significant differences between the two sides,” a House GOP aide said.

The GOP aide said that as a technical matter, both the House-passed budget and Senate-passed budget are in the U.S. Senate. For this reason, the House cannot take up a motion to establish a conference committee.

Murray declined to explain Thursday why the Senate has not yet sent the budgets over to the House. No legislative vote is necessary to do so.

Aides said Murray is eager to have a conference committee, and White House acting budget director Jeff Zients on Thursday also endorsed return to regular budget process as the best way forward for debt talks this summer.

The White House does not want to have a high stakes negotiation connected to the debt ceiling, which needs to be raised sometime after May 19.

Boehner plans to consult with his members in the coming weeks on how to proceed on the debt ceiling, aides said.

Budget committee member Rep. Tom Rice (R-S.C.) told The Hill is he is eager to serve on a conference committee, but when he asked Boehner last month to join the panel, the Speaker did not yet know if a committee would be created.